{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Principal Component Analysis - Key Ideas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PCA finds principal components as linear combinations of the existing features and uses these components to represent the original data. The number of components is a hyperparameter that determines the target dimensionality and needs to be equal to or smaller than the number of observations or columns, whichever is smaller. \n",
    "\n",
    "PCA aims to capture most of the variance in the data, to make it easy to recover the original features, and that each component adds information. It reduces dimensionality by projecting the original data into the principal component space. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports & Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:45.977727Z",
     "start_time": "2020-06-18T13:40:45.975685Z"
    }
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:46.613413Z",
     "start_time": "2020-06-18T13:40:45.979430Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from numpy.linalg import lstsq\n",
    "from numpy.random import randn, seed\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Patch\n",
    "import seaborn as sns\n",
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:46.617329Z",
     "start_time": "2020-06-18T13:40:46.614945Z"
    }
   },
   "outputs": [],
   "source": [
    "sns.set_style('white')\n",
    "seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Linear Projection: Principal Component Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The PCA algorithm works by identifying a sequence of principal components, each of which aligns with the direction of maximum variance in the data after accounting for variation captured by previously computed components. The sequential optimization also ensures that new components are not correlated with existing components so that the resulting set constitutes an orthogonal basis for a vector space.\n",
    "\n",
    "This new basis corresponds to a rotated version of the original basis so that the new axes point in the direction of successively decreasing variance. The decline in the amount of variance of the original data explained by each principal component reflects the extent of correlation among the original features. The number of components that captures, e.g., 95% of the original variation relative to the total number of features provides insights into the linearly independent information in the original data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below figures illustrates several aspects of PCA for a two-dimensional random data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Create Noisy, Correlated Data from Signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:47.051089Z",
     "start_time": "2020-06-18T13:40:46.618465Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 504x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_signals = 250\n",
    "x1 = np.linspace(-10, 10, n_signals) + .1 * randn(n_signals)\n",
    "x2 = 1.5 * x1 + 2 * randn(n_signals)\n",
    "data = pd.DataFrame({'$x_1$': x1, '$x_2$': x2})\n",
    "ax = data.plot.scatter(x=0, y=1, s=10, title='2D Noisy Data', figsize=(7,8))\n",
    "ax.set_aspect('equal')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Compute Principal Components "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:47.059589Z",
     "start_time": "2020-06-18T13:40:47.052075Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.54381787, -0.83920327],\n",
       "       [ 0.83920327, -0.54381787]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA()\n",
    "pca.fit(data)\n",
    "pca.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:47.076935Z",
     "start_time": "2020-06-18T13:40:47.061034Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.00024229,  0.03183435])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean = pca.mean_\n",
    "mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:47.098438Z",
     "start_time": "2020-06-18T13:40:47.078696Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.54381787],\n",
       "       [-0.83920327]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pc1, pc2 = np.split(pca.components_.T, 2, axis=1)\n",
    "pc1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Check share of explained variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:47.107993Z",
     "start_time": "2020-06-18T13:40:47.099404Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.98929523, 0.01070477])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Components are orthogonal to each other"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:47.115980Z",
     "start_time": "2020-06-18T13:40:47.108974Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(pc1.T, pc2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plot Principal Components as new Basis Vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below figure shows how the first and second principal components align with the directions of maximum variance while being orthogonal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:47.123580Z",
     "start_time": "2020-06-18T13:40:47.117005Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "l1, l2 = pca.singular_values_ / 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:47.404717Z",
     "start_time": "2020-06-18T13:40:47.124806Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = data.plot.scatter(x=0, y=1, s=15, title='Principal Component Vectors', figsize=(6,8))\n",
    "ax.set_aspect('equal')\n",
    "origin_x, origin_y = pca.mean_\n",
    "dx1, dy1 = np.squeeze(pc1.T) * l1\n",
    "dx2, dy2 = np.squeeze(pc2.T) * l2\n",
    "pc1_arrow = ax.arrow(origin_x, origin_y, dx1, dy1,  width=.2, color='k')\n",
    "pc2_arrow = ax.arrow(origin_x, origin_y, dx2, dy2,  width=.2, color='r')\n",
    "plt.legend([pc1_arrow, pc2_arrow], \n",
    "           ['Principal Component 1', 'Principal Component 2'], \n",
    "           fontsize='small')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Project 2D data onto the first Principal Component"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following figure demonstrates how the first principal component minimizes the reconstruction error, measured as the sum of the distances between the data points and the new axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:47.768026Z",
     "start_time": "2020-06-18T13:40:47.405865Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x864 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# de-mean data, convert to numpy array\n",
    "data_ = data.sub(data.mean())\n",
    "X_ = data_.values\n",
    "x_, y_ = X_.T\n",
    "ax = pd.DataFrame({'$x_1$': x_, '$x_2$': y_}).plot.scatter(x='$x_1$', \n",
    "                                                           y='$x_2$', \n",
    "                                                           s=15, \n",
    "                                                           title='1D Projection', \n",
    "                                                           figsize=(6, 12))\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "# plot first component\n",
    "t = np.linspace(-25, 25, n_signals)\n",
    "pc_x, pc_y = t * pc1\n",
    "ax.plot(pc_x, pc_y, c='k', lw=1)\n",
    "\n",
    "# project original data on first component\n",
    "proj_x, proj_y = (X_.dot(pc1) * pc1.T).T\n",
    "ax.scatter(proj_x, proj_y, s=15, c='k')\n",
    "\n",
    "# plot link from data to projected points\n",
    "lines_x, lines_y = np.c_[x_, proj_x], np.c_[y_, proj_y]\n",
    "ax.plot(lines_x.T, lines_y.T, lw=1, c='darkgrey')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plot 1D Representation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:47.930159Z",
     "start_time": "2020-06-18T13:40:47.769010Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "projection1D = data_.dot(pc1)\n",
    "ax = projection1D.rename(columns={0: '$z_1$'})\\\n",
    "    .assign(x2=0).plot.scatter(x='$z_1$', y='x2', s=10, title='1D Signal')\n",
    "ax.get_yaxis().set_visible(False)\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Compare to Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the below figure contrasts PCA with supervised OLS, which approximates the outcome variable (here we choose x2) by a (one-dimensional) hyperplane computed from the (single) feature. \n",
    "\n",
    "The vertical lines highlight how OLS minimizes the distance along the outcome axis, in contrast with PCA that minimizes the distances orthogonal to the hyperplane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:48.322879Z",
     "start_time": "2020-06-18T13:40:47.931504Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x864 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = pd.DataFrame({'$x_1$': x_, '$x_2$': y_}).plot.scatter(x='$x_1$', \n",
    "                                                           y='$x_2$', \n",
    "                                                           s=15, \n",
    "                                                           title='PCA vs OLS', \n",
    "                                                           figsize=(6, 12))\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "# get OLS line\n",
    "reg_X = np.column_stack((x_, np.ones_like(x_)))\n",
    "(m, b), _, _, _ = lstsq(reg_X, y_)\n",
    "reg_y = m * x_ + b\n",
    "ax.plot(x_, reg_y, c='k')\n",
    "\n",
    "# plot residuals\n",
    "lines_x, lines_y = np.c_[x_, x_], np.c_[y_, reg_y]\n",
    "ax.plot(lines_x.T, lines_y.T, lw=1)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Combined Figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below figure is included in the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:49.248232Z",
     "start_time": "2020-06-18T13:40:48.323962Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(ncols=3, figsize=(14, 6), sharex=True, sharey=True)\n",
    "\n",
    "title='Principal Component Vectors'\n",
    "data.plot.scatter(x=0, y=1, s=15, ax=axes[0], title=title)\n",
    "axes[0].set_aspect('equal')\n",
    "\n",
    "origin_x, origin_y = pca.mean_\n",
    "dx1, dy1 = np.squeeze(pc1.T) * l1\n",
    "dx2, dy2 = np.squeeze(pc2.T) * l2\n",
    "pc1_arrow = axes[0].arrow(origin_x, origin_y, dx1, dy1,  width=.2, color='k')\n",
    "pc2_arrow = axes[0].arrow(origin_x, origin_y, dx2, dy2,  width=.2, color='r')\n",
    "axes[0].legend([pc1_arrow, pc2_arrow],\n",
    "               ['Principal Component 1', 'Principal Component 2'],\n",
    "               fontsize='small')\n",
    "\n",
    "# de-mean data, convert to numpy array\n",
    "data_ = data.sub(data.mean())\n",
    "X_ = data_.values\n",
    "x_, y_ = X_.T\n",
    "pd.DataFrame({'$x_1$': x_, '$x_2$': y_}).plot.scatter(x='$x_1$',\n",
    "                                                      y='$x_2$',\n",
    "                                                      s=15,\n",
    "                                                      title='1D Projection',\n",
    "                                                      ax=axes[1])\n",
    "axes[1].set_aspect('equal')\n",
    "\n",
    "# plot first component\n",
    "t = np.linspace(-20, 20, n_signals)\n",
    "pc_x, pc_y = t * pc1\n",
    "axes[1].plot(pc_x, pc_y, c='k', lw=1)\n",
    "\n",
    "# project original data on first component\n",
    "proj_x, proj_y = (X_.dot(pc1) * pc1.T).T\n",
    "axes[1].scatter(proj_x, proj_y, s=15, c='k')\n",
    "\n",
    "# plot link from data to projected points\n",
    "lines_x, lines_y = np.c_[x_, proj_x], np.c_[y_, proj_y]\n",
    "axes[1].plot(lines_x.T, lines_y.T, lw=1, c='darkgrey')\n",
    "\n",
    "pd.DataFrame({'$x_1$': x_, '$x_2$': y_}).plot.scatter(x='$x_1$',\n",
    "                                                      y='$x_2$',\n",
    "                                                      s=15,\n",
    "                                                      title='PCA vs OLS',\n",
    "                                                      ax=axes[2])\n",
    "ax = axes[2].set_aspect('equal')\n",
    "\n",
    "# get OLS line\n",
    "reg_X = np.column_stack((x_, np.ones_like(x_)))\n",
    "(m, b), _, _, _ = lstsq(reg_X, y_)\n",
    "reg_y = m * x_ + b\n",
    "ax = axes[2].plot(x_, reg_y, c='k')\n",
    "\n",
    "# plot residuals\n",
    "lines_x, lines_y = np.c_[x_, x_], np.c_[y_, reg_y]\n",
    "ax = axes[2].plot(lines_x.T, lines_y.T, lw=1, c='darkgrey')\n",
    "\n",
    "sns.despine()\n",
    "fig.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Recover Data using Inverse Transformation 1D => 2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:49.476817Z",
     "start_time": "2020-06-18T13:40:49.249492Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9+/eHUqlEbm4uNm/ejKKiIvTv3x8dOnTAzJkzsWLFCrz44ovYuHEjrly5gpkzZ2L+/PkICgrC/v37sWjRIsydOxeDBg1CQkIC/vjjD4SHhyM7Oxu//fYbNm3aBA6Hg2HDhqFjx44AdFbUsGHDcPDgQYvvu3DhQixbtgyNGjXC7NmzHfyJEe4ICUwF0a5dO6xYsQL3799HXFwc/Pz88O+//+LSpUtsV3i1Wo2bN28iPz8fL774IgBg8ODBAHQd5/UO0zZt2mDZsmWoXr06goKCcPr0afz888+YMmUKLl++jJs3b2LYsGEAdBMa9f1q9Tkp1t43Ly+PvadVq1al6nNLEMVBPpgKpmbNmliyZAlmzJiBOnXqICwsDBs2bMC6devQtWtX+Pn5oW7dupBKpQCAb7/9Fqmpqahbty7++ecfAMDJkycREBAAAOjfvz/WrVsHhUKBF198ES+88AICAwOxfv16bNiwAX379mXHguhDxy+88ILF95VIJLhy5QoAlPvYWIIAqoAF4+vrW+5hansJDAzEkCFDcODAAdSvXx+DBg3CkydPEBERAW9vb3z66aeYPn06uFwuJBIJhg0bhueffx5z584FwzDg8XhYsGABAKBt27aYOXMmxo4dCwBo1qwZ2rdvj9jYWCiVSgQHB5vt8c0330RaWprZ+y5ZsgRTpkyBl5cXvLy8jMbiEs5NakYeDv0nQ6fGEkQ2t/93srJw+zwYovKgz75ySM3Iw/iUdMhVGogFPHwVG+q0IkNHJIJwMQ79J4NcpRs8J1dpcOg/mYN3ZB0SGIJwMTo1lkAs0I3sFQt46NRY4uAdWcftfTAE4W5ENvfFV7GhLuGDIYEhCBcksrmvUwuLHjoiEQRRYbi9wCieOsOcdT2CcGfc/ogkEvAQMPXXcltPuqh7iffk5ORg8eLFePDgAVQqFZo1a4ZJkybB29vb6L7MzEz88ccfGDdunMV1/v77b9y6dQsDBgywa49vvvkmfv/9d3h4eLDXhgwZArlcDrFYDJVKBT8/P3zyySeoWbOm1XW2bNmCvn37UhtMotS4vcBUNgqFAu+99x7mzZuHli1bAgB+/vlnfPTRR0hKSjK6NygoqNi8kddee61c9/b555+zJQm7du3CrFmzkJiYaPX+pKQk9O7du1z3QFQtSGDKmb/++gtt2rRhxQUA+vTpg5SUFOTk5GDlypVslXN8fDx+++03rFixAtu2bcPGjRtRvXp1CAQCdOvWDQBw9epVDBw4EB999BHq1auHnJwcvPzyy/j0009x+/ZtzJkzB0VFRXjw4AESEhIQERFh0z579uyJL774AkVFRTh37hy+/vprADqB/Pzzz3Hq1CnIZDJ8+OGHSExMxKxZs3D79m3cv38fr732GiZMmFD+Hx7hdpDAlDM5OTlo2LCh2XU/Pz/cvHkTwLMqZ30P4nv37mHNmjXYuXMnhEIhhg4davZ6qVSK5ORkiMViREREQCaT4erVqxg+fDjCwsJw5swZJCYm2iwwAODj44NHjx7hv//+w5IlS+Dr64vVq1dj7969GDt2LFatWoUVK1bg1q1bCAkJQUxMDIqKikhgXBBHlRaQwJQzvr6+OH/+vNl1qVSK5557DgDMOu9nZ2fjxRdfhFgsBgCEhoaavb5hw4asD0cikaCoqAgSiQSrVq3C9u3bweFwoFarbd4nwzC4e/cuateuDV9fX8yfPx+enp7Iy8tDq1atjO6tUaMGLly4gOPHj8Pb2xtKpdLm9yEcj2FpwbZTuZVaWuD2UaTK5q233sLRo0eNRGbbtm2oVasWGjRoAMC8QXbDhg1x9epVKBQKaLVaiwJlqan2l19+iV69emHJkiUICwuDPWVl27dvR7t27cDlcjFjxgwsWLAAixYtQt26ddl1OBwOtFotduzYgWrVqmHZsmWIi4uDQqGw670Ix+LI0gK3t2AUKo1NkR971hM9TdO2hJeXF1avXo0FCxbgwYMH0Gg0aNq0KZYvX271NbVq1cLIkSMxaNAg1KhRA0VFReDz+SVaJF26dMH8+fORlJSE+vXr4/79+8XeP2XKFNZK8vX1ZZtM9erVC/3794ePjw/q1KmDO3fuAABat26NUaNGYdasWZg4cSJOnz4NsVgMf39/3Llzp1SV5UTloD8SVRMJkHPvCYQ8LpQarc2lBTKZDFKpFAEBAZBISl+KQNXUToBarcZ3333HtmAYPHgwJkyYgDZt2jh4Z/bhip+9O2J4JNIj5HHRIbA2BoX5l3g8SklJQXx8PIRCIZRKJZKTkxEbG1uqvbi9BeMK8Pl8yOVy9OnTBwKBAMHBwaUePEcQhkciPUqNFg1qeZYoLjKZDPHx8ZDL5ZDL5QCA+Ph4RERElMqSIYFxEiZOnIiJEyc6ehuEG9CpsQTbTuUaiYytR6P09HRwucauWYFAAKlUSgKjh2EYmjRYybjwSdvtMKy2riYSoEChsik8rT8a6S0XPSqVim3Zai9uJzAikQj5+fk0n7oSYRgG+fn5EIlEjt4K8RR7q60Nj0aGiEQiJCcnl9rR63YC4+fnh9zcXMhkztvlyx0RiUTw8/Nz9DaIUiKVSsHnG8uBl5cXduzYgc6dO5d6XbcTGIFAYJbIRhBE8Rw8eBAFBQVG17RarcWkT3ugRDuCqOIkJSVh8uTJZtdXrFhRphwYgASGIKo0MpkMH3zwgdl1Ly8vs5KR0kACQxBVGKlUCqFQaHZdrVaXOnJkCAkMQVRhAgICLJakfPnll2U+HgEkMATh1qRm5GHWLxeRmmF5uqlEImHbgHh7e8PDwwOrV6/G6NGjy+X93a4WiSAIHaYTIOM6NrKadFdexY2muF2YmiAIHaZtGlYfvAKNlsHWkzmIC+IgRMJFaGgoJBIJ+6e8oSMSQbgphhMgeRxAo9UdVhRqLRb9sBNRUVHw8/NDSkpKhe2BBIYgXIiSfCqG6GuShrb3x5g3AiHi677uWpUCCmk6AECpVCI+Pr7CMt8dekQ6d+4cli5dig0bNuDSpUsYM2YMGxqLjY1lG18TBFG61peGNUleChk+TdqCgv/SIM9KY+/hcrmlrpYuCYcJzHfffYddu3axHdYyMjIwfPhwxMXFOWpLBOHUWGt9aWsz75hXm+KjgWugUCiMrmu12nLJebGEw45IDRs2NJrJc/HiRfz1118YPHgwpk+fjsLCQkdtjSCcEkOfiljAQzWRAONT0rH+2HWMT0kv8dgkkUiwdu1ao0F6QqGwTNXSJeEwgYmKijKq3gwODsbHH3+MjRs3okGDBli5cqWjtkYQTomhT+Wr2FAUKFR2N/OOjY3FjRs3sG/fPuzbtw+5ubmlbodpC04Tpo6MjISPjw/797lz5zp4RwThfJj2edF3riuuY51pjotEIilTCwZ7cJooUnx8PDuu49ixY3jppZccvCOCcG5MLRpLPpikpCQ0aNAAb7zxBvz9/Ss0JG0Jp7Fg5syZg7lz50IgEKBOnTpkwRCEDRTXuS4pKQljxowBAIgD20IUEIrRn60sdQPv0kClAgThBJQ02tXe0a8ymQz169eHRqOBOLAt6vT8GFyBCFq1EsF1hfggunWlTHd0miMSQVRV9Pkt1qJBJT1viQMHDkCj0TmARQGh4Ap0/ZK5fCEu3oPN65QVEhiCcDAljXa1d/RrSkoKhg4dyj5WSNOhVRnnvlTWCFkSGIJwMKb5LabRoJKeN0Q/HaCoqIi9Js9Kw91di/EkKw08MDatU144jZOXIKoqhnOMLPlYSnrekKSkJLPRIwCgkp7B3ElxeKFTG7t8OWWFnLwE4SbIZDI0bNiQLQXQR440Ny7i+E/fOWRuOFkwBOEmJCUlGYmLPnLEe6UbcplaqHx5IR8MQbgFMpkM8+fPZx8bRo404FWKQ9cSJDAE4YKY9oU5cOCA0fOGkSNrDl17esuUFvLBEISLYdprV5K1B6dOnYQoIBQKaTrb66V6UEeMnLUcnYMbmjl0TdewpbdMaSAfDEG4GKZ5Mf+oarP+Fu/gSNzdtRjanHNYNfM9xA5sY9Mah/6TVYjA0BGJIFwMw7wY/TGIzdQViCAKCMWSJUuKbcNgT25NWSCBIQgXQ58X4ye/gru7FqPw3F5WaPT9diMiImxao7hK7PKAjkgE4YKESLh4O0CDI0/9LXd3LWZ9MG82ldiU81JcJXZ5QQJDEC7GzNXbkPTLQWhvZrDX5Fm6Rt6NGzfGnj0nHLg7Y+iIRBBOiqUw8vZj/2Ldf1x4tuwKz4gEiAPbQigUYvDgwdi9ezf+/fdfu9araEhgCMIJsdaiYfH6XWYOXZFIhA8++ADR0dF2r1fRkMAQhBNiKYycmZmJi/u3mTl0i4qKShw7YrrephPXK3T/ekhgCMIJsRRG/vzzz9nWC49O78bdXYsBAG3HLMVZmbbE9YS8Z1/3I1n5WLLvMmXyFgdl8hLujGGbzKuHdrL9dfUYFjTako07/Ps0HLj8rCaJx+VAo2UqNJOXLBiCcEIMxSVEwsX48ePN7jEsaLSlQ92gMH/WKuJxAI2Wsfm1pYXC1AThZJjOoG6tugClUml2n0KajjptekCpNc7GtdYg3LBxVTWRAGsPXytxplJZIYEhCCfD1CH76+krFu9TSc9gQY/GOH9HyYqJqTiZHn0Mk+tCGtSo8O52JDAE4WR0aixhJzbqI0WmeDVpj+gRk1C9enV81l4nDqkZeVi67x+bixgrI5OXfDAE4WTojzIBquu4u2sx235Bj3fTV/F8vxk4nu/B5rToLZfLeYXsfZXV2Ls4yIIhCCdk87LpOLh2rcXnOg8Zj9MF5g5aveUCAE19vTEpqlmlNPYuDrJgCMLJyMzMxFor4jJ16lSM6fOGWY6Mad5MRPN6OPSfrFLLAixBFgxBOBlpaWkWr3s3fRXqln0BwOIYE0sRIkuO3sqELBiCqERsKTh86O2PmhGjIQ5sy14TB7aFb++p2Hb2Dsan6Jy+n/VqYRYh+qxXCxQoVHZNgqxISGAIopKwpeBw5uptWHb0Hnxe6YE6PT9mRSa06yCon35dSxKNyupWZwskMARRSZQ0Y1omkyHpl4PgCDwA6KqlPV94BYcPH8acMQNtFo3K6lZnC+SDIYhKwjC/xZJI/PLLL1BIz0LUPBxcgUhXNX07E0KhEB2KGR9rKXO3MnJcbIGKHQmiErGWxv/qq6/i2LFjAJ6NfFVI04EbF3D9+nVIJJYtlsoaP1JayIIhiDJiTTQsYcmyiI6Otigu2pxz+P77762KC1B540dKCwkMQZSBkmp/invdof9kyL94GL/++isA4/YL3i2j4MvcR52Wbxa7jqVjlz2CV9GQk5cgykBJjltLGEaTdt+TsJEiw/YLXL4QMoFvie0tTR26ABzSGtMaJDAEUQZKExI2FCV9X13g6TxptXFbBltES5//Etnct1SCV5GQwBBEGShNSNh0MqO+WlqelQaF9KzRvTwuB9VEAptbWzpTDgzg4CjSuXPnsHTpUmzYsAHXr1/H1KlTweFw0LhxY8yePRtcbvH6R1EkwpGUxdeRmpGH/53Pxuo5E1B4+Sh73bNxO/jFzESRhgEXgF8tT9x+qIBSo7U5SkQ+GADfffcdZsyYgaKiIgDAwoULMWHCBGzatAkMw+CPP/5w1NYIokTKOgYksrkvlgxsg29nj4NIJIKXlxdEIhHWfDoeXw9+BeFNJeDzuMi+9wRKja6ht61HHsMjk6NxmMA0bNgQiYmJ7ONLly6hbVuds+u1117D0aNHrb2UIByOLb4Oa3VHe/bswYgRI7Bnzx7ExsYiOzsbBw4cQHZ2NmJjYxHZ3BcNanmywqLHGY489uKwMHVUVBRyc3PZxwzDgMPhAAC8vLxQUFDgqK0RRImUlJVrLXz98ssv4+LFiwCA5ORkvPzyyzh//rxZrovh+kIeFx0Ca2NQmL9TWCX24DR5MIb+lsePH8PHx8eBuyGI4oksJnUfsGzhFF09yYoLoMt7yfUNxYJ1ezD93Wi71jfFmfwuhjiNwDRv3hwnTpxAWFgY/v77b7Rr187RWyKIYimu3seShTNn5Gj2ecOkujUZarTJyDNby9Z6otIm+1UGThOmnjJlChITEzFgwACoVCpERUU5ektEFaS8BsSbhq/P/bbByK9omFSn5fDLlK/ibNAUA80AACAASURBVLkvhjjUgvHz88PWrVsBAI0aNcKPP/7oyO0QVZzytgT0FkhSUhImT55s9JxCmg7v4Eh2KmNZnLcl+YMcidMckQjC0ZR34SCb67Jivdlz8qw03P91GcbM+RKdgxuy71MaX4q9/prKhASGIJ5SnpaAoTVUs/tEaDRqs/EjSz98F6MHtrH4GnstKGfp/2IKCQxBPEVvCWw6cb3Ma1mrN9K3YvhsdAxGj9Y5ffVWS869J07deqE0kMAQhAnHr96DXKXB8av32Aple48fnRpLsOn4NagZLrQqBbRFj9moUY3QrmjZTRclNbRahDwuhDwuWxbgTL6U0kICQxAGmPphNp24zgqOPceWEAkXHTiXsftUFhTSdOOoEZfPWieG76fUaBHeVIIGtTwtipmz5roUBwkMQRhg6ocBYPexJSUlBcOGDYNSadx6QR81EvG5rHVi+n7WsnWdOdelOEhgCMIA04gM8OzIZHpsMbUo9FGj7+Z+YyYu8qw0PPhtBbrFTUR89w5GzbltiQA5e2tMa5DAEIQJphEZS45fU4sirmMjdpqiT9cJUKqURlEjkUiE7V/OQufOnUt8P0s4c65LcZDAEIQNmDp+TS2K/Rm3zaJGhgLDMAxCQ0Ntei9rY0icNdelOJymVIAgHI21MgFLxxNLw+ah0R2LDLvU6ZkxYwYkEkmJpQjF9Zlxpj4vtkIWDEGgeCeqpeOJqUVxZOsq3Nn5O5vnYno8Gj16tE2OWlf1tViDLBiCQPEFg9b67uotihAJF59++qku/X9/EgCww+u5XC7Wrl0LiURiU1Gis/XULStkwRAESnai6kVFLwqGVsW8efPYv1fv9A6qh/UDh8eHd3Akgu4fR2xsrNl78DhANZHAzN/iqr4Wa9DoWIJ4iqWws2G42tKIVplMhueeew5qtRriwLaQ9J4ODu/Zv9uRAUL0fy2YXedszgOsPngFGi0DIU93gLCnoberQRYMQTzFMFxs6i9p90Iti76RAwcOsN0YRQGhRuICrQZNGjU0W0ej1f2bbthz1x38LZYggSGIpxhaLKb+EkDnEzE8Qr3//vtI3psGr9eGgydNN+rxAkaLhLeaokChsrqOqQXj6v4WS5DAEAQsJ84ZCsqgMH8MCvNnBciPcw/Je9OezZIOjsTdXYtx/9dleGPgWIzv35k9ZpmWAjR/rjr2Z9xGRPN6CGlQw238LZYggSEImEeRChQqi85W/X9bt+4OUUDrZ7OkBSJ4t+yCkU3VmD9nCLuupdIDfcZv9r1r+Co2FJ/1alGZP2qlQmFqgoDl8HBkc1/2uGSY8LZ06VKcPn3abJa0OCAEMmF9s7WdeXZ0RUMWDEHAciq+pcS4EAkX06dPB/BslrRnoG5gIIcvhEfDlsW+j6vWFJUWEhiiymIpB8XQD2LJ2rh/MYMdEAgAhef2QuQfDK5ABK5WjZ5hTYp9T3fLcykJOiIRVRJbZkubHpsyD+zAgAEDjFoxyLPScHfXYkgeZCBpWDubBMMVa4pKC1kwRJXElpofQ2ujkUiBuC6zzdbh8/n4bHQMJk2aZPW9XLETXXlBFgxRJbG15kdvbRT+e8zi88uXLy9RXBI2nsH6Y9eRsPGM3QPdymsQnKMgC4aoktjjC0lKSrIqIhEREcW+z6YT19mMXaVGi00nrttsxbhqm0xDSGCIKostneSSkpIwZswYi8+NGzcOQUFBFbE1AO7RuoGOSARhBZlMhnHjxpldF4lE2LJlCxITE0tcY1CYP1sSIORxMSjM3+b3d4fWDWTBEIQV0tPToVarza4LG72Ck9pGqJmRV6JFEdncFysHtyqVk9cdQtokMARhB+LAtqjT82NsO3sHey7l2+QXKctYV2cdCWsrdEQiCCuEhoZCIBAYXfN84RVo8Gxekrun+pcVEhjC5amoUK5EIsG6desgEong5eUFkUiEsX3CXd4vUplQRzvCpTEM5VZUVziZTAapVIqAgAB2MkBJfpGqnFxnCPlgCJemvEO5MpkM6em6kSOhoaGQSCTsHz0l+UXcIX+lvCCBIVya8qhO1lsbzK1MfPHFFxA0eBkKaTo02Wfxww8/sE27bcUd8lfKCzoiES6PpeNIcUcUa828tWolONC1XdCqFLi7azFw4wKuX79uZMHYsp+KPra5CmTBEC6P6ZGluCNKcc28uXwhu4Z+/Kvy1iVIpVK7BMYd8lfKCxIYwu0o7ohiqZm3kAcoNbr50fpeL1q1Ujf+VatFQECA3Xtw9fyV8oLC1IRLUVxIWv9cNZHAaii5msg4r6X5c9Uh/2Mliu5cM2okpbojhbhRK3y0fJ1d1gthjNNZML1790a1atUAAH5+fli4cKGDd0Q4C7YefcQCHuI6NkKBQmV2RClQqIzW3PvHX8g98TvE+fnshACtWglh3QB4PNcE22/w8JoNJQGEZZxKYIqKigAAGzZscPBOCGfEnqNPgUJlsVu/YdSJz9Hi2M9rda952plOFBAKfnVfts9uVY8ClRWnOiL9888/kMvliIuLw9ChQ3H27FlHb4lwEJaOQsVVFxf3nOFaegdsTEhd5P28EPKsNPY+/fD6wnN7wYPG4lqEfTiVBSMSiRAfH4+YmBhIpVKMHDkSe/fuBZ/vVNskKhhrR6GSojPtXqgFQNciwVrUSL/Wnxu+QOFly13qQiQ8fDo0zOYoEGXtWsepvrmNGjWCv78/OBwOGjVqhBo1akAmk6F+ffNZM4T7UtxRyFJ0xtT/YthzxdJaIRIuli5davG9Bw8ejB9//JF9r5KgrN3icaoj0vbt27Fo0SIAQF5eHgoLC8mDXwWxt9FSccPMLK2VkJBgsc8Lj8fDihUr7NprVRukZi9OZcH069cP06ZNQ2xsLDgcDhYsWEDHoyqIvYlqxZULmK7lx7mHbdu2WVxn5cqVNv2DZngkqmqD1OyFSgUIp6K0/gxbX5eYmIjx48ebXR8wYAA2b95c4toAzMoAAJAPxgpkHhBOQ1n8GbZkzmZmZuLMmTMWn+vbt69NezIsLdAfiarKELXS4FQ+GKJqU5H+jPfffx+v9ByGX3I9IH6a46KHy+UiPDzcpj0BMPPpmIbUXX2WUXlCFgzhNFSUPyMzMxPJe9PYTF3v4Ejc3bUY8qw0eHh44Pvvv7fqezHd06AwfwwK87d4ZNp2KhdxHRth7eFrFFV6CgkM4TRUVBXyqFGjIAoIBVcgAvCsUlp9PR27du1C586d7d6T/r+zfrloZOHsz7hNvWAMIIEhnIryrkLOzMzE4cOHIQ5Uwjs4ElyBCIxGDW3RYwC6rnVl2ZOphRPRvB6y712jqNJTSGAIl8TWqNHPP/8MQFcG8OjkTlQP6wcOjw+fNr0xondEmfOsLFk4IQ1qUFTpKSQwhMtha7Tp/fffx9dffw1xYFu2iJHD0/3KcwUieL7YtFz2Y2rhUC+YZ5DAEC6HLT1vMzMzWXExbMPAqJXg8IVGx5fS5N5Q/ZFtUJiacDlsKSX48ssvAcDYucsXoqGHAkPb+7NWj94aWn/sOsanpNsUWi7Na6oqJDCEy6H3e+iFAoBR3klmZibWrl0LcWBb8Kv7glErAQBalQJxrzU2SowrTe4N1R/ZDgkM4ZJENvdlG0oZWhMzV2/DSy+9BL5/KOr0/BiegW3BAHiSlYam+UcxPKq10Tr2FlaW9jVVFfLBEC6NqTXxzU9/gmEYs6MRU3gXm1bNMXt9aXJvaGqA7ZDAEE5DaRynhnkoPEYDuVRXa6SQprN5L1qVAr3bNbUaki5N1IciRbZBRyTCKSit49SwBebtnxewLTD1PXYfnd6NwtO7UKNZe3LGOgASGMIpKIvjNLK5L3hnf8KT/04AAMSBbVEzYjQAnSVTq10/bDt7p1wiPlTIaB90RCKcgrIUOspkMrYFpmHei3dwJKo9uYXHT/8dLWttELXHtB+yYAinwDT0bM8Xd/ny5dBodNaPaVFjSEhIuUV8KDxtP2TBEE5DaRynMpkMy5cvZx8bOnd50GBYp8YYBssd5+x1KlN7TPshgSFcGqlUCg8PDyiVumQ6vXPX84VXsHrOBLP2CnpKc9yh8LT90BGJcFkyMzNx/PhxqFTG42DlWWmY37clqlevbtUhW9rjjj7Bj8TFNsiCIVwGwyPNrlXz8PXXX7PP8fl8iEQiqFQqfPnll3ihU2+LFop+jWoiAcQCHh13KhgSGMIlMDzSbEnLRs7eNKPn1Wo1kpOTER4eDolEYtZpTm+hGE4EiOvYCAUKFR13KhA6IhFOhbU8E8MjTZGGQfVOQ8yad8vlcjZb11K9kOmxqEChouNOBUMCQzgNxWXzGgoGwzDwqNsIdXp+bCQy2novmQ25Nwx7WxIdSpyrWGjwGuFw9H6RnHtPcODyM2fr0Pb+bMW0/r5PthzHnaJnJ/tHp3fj/v4ktOs7Eg+a9zUaiGbJMilpiBpZM+ULWTBEpWDNUjC0Wo5k5UPI0/1KWnK8hki46Pq8GlqVAoCuv4tCmg4AaB09xKaokGEUiBLnKh5y8hIVTnE5J4ZfcqVGi/CmEjSo5WnmeE1JSUF8fDyEQiFUdYPg4d8SCmk65FlpGDduHHqGNcH+q+l2RYUoca7iIYEhKpzieuhaGmxmekyRyWSIj4+HXC6HXC4HHh6HJjsdS5YsQUTEDwgKCgIA6uvihJDAEBVOcZaCLV/y9PR0cLnGp3kPDw+0a9eOFRf9WtTXxbkggSEqnJJEpLgveUpKCoYPH46ioiKj6yqVCgEBARW1ZaKcIIEhKoXSFjIOHToUarXa6LpYLEZycnKZh6YRFQ8JDOG0zJs3z0xcAOCHH35A//79HbAjwl4oTE04JUuXLsVXX31l8bkaNWpU8m6I0kICQzgdk5avw4J9WWalAAAgEAhsGlhPOAckMIRDMU3A237sX2y94Q2fV3qYlQIAQGJiIs7KtJTe7yKQD4ZwGJYS8PacyjJqeSkKCGUnBSxZssRqGwbCOSELhnAYlhLw6mrzLZYCjBgxApMmTaL0fhfDqSwYrVaLOXPm4PLlyxAKhZg3bx78/f0dvS3CBmztb2t4n2kCXv7Fw1g18z2IXmwDUUAoWwoAADExMQCMk/aEPC5y7j1hq6cJ58Opqqn/97//4c8//8SiRYtw9uxZJCUlYdWqVVbvp2pq58DwqFNSJbPpfYDOkjm7dzN2r55vcX2hUIiNf13A+TtKNgt40wldcaRSo6VKaCfGqY5Ip0+fRqdOnQAAISEhuHjxooN3RNiCrccWazVJsU14VsVFIBDg4y9/xMzfrrJ9YgCgQS1PKDVaq+9JfV6cA6cSmMLCQnh7e7OPeTyexUQrwrmw1MippPt4XA6qiQQAgP3791tde86cOeDUDzITpuLes7RjaInyx6l8MN7e3nj8+DH7WKvVgs93qi0SFrC1KjmyuS/iOjbC6r+yoNEyWHv4Gh5dO48VX6egZsRoI5+Lnj59+iCXqWVWLFncexZXvU1ULk717W3VqhUOHDiAbt264ezZs2jSpImjt0TYiK21RgUKFTRPvX5ylQZrjt1A7Z5TwOHx4R0cibu7FrMiM27cOOQytXDoP5nFBt3W3pP6vDgPNgvMkSNH8Pvvv2Pw4MEICgrCli1bMGDAgHLdTGRkJI4cOYKBAweCYRgsWLCgXNcnHE+nxhJsTsuBUqMFB1oIfV8Ah6s76ujzXpTXTmPTpk2o2eJ11iks5HHRIbC2Te9BfV6cB5sFZtOmTVi4cCFWrVqFBw8eIDMzs9w3w+Vy8dlnn5X7uoRzotUyrLgAAKNRQyFNB4fDQXh4OBKP5hl1uztwWYbjV+/ZPIWRhMXx2OzkrVWrFnx8fDBlyhQcOXIEFy5cqMh9EW7Kof9kbPSHw+WB0eic+IxGjYcntkOelYaFCxdCIpEYOXL1GEaMKFLk/NgsMK+//jr790mTJqF3794VsiHCvenUWAI+RycwWpUCD09sx6PTuyHbuQAPD/2IHj16YNKkSQCeHXXCm0rMmoFTpMg1KDHRbv78+Zg+fTo4HE5l7clmKNHOuTDN5rWW3TtuYRI2/ZluFjXi8/m4efOmxUZSpmvN+uUi1h+7zj5vrVk44VhKtGA8PT0xduxYXbNlAIcPH8bAgQMrfGOEa2FqUSzZd9mihZGSkoL16zdYXGPSpEmsuCzZdxlRKw5iyb7LAMyHzhsen4Q8Lo5k5ZM144SU6OT98MMPsXv3brzzzjsQCoXw9PRkTViC0GOae7I/47ZZLkqIhIux81ahRrcPwRWIjMLSfD4fEydOBKATl5UHsgAAl/N0/50c1dTo/QwjRYYD2yjvxbko0YI5duwYtm7dCk9PT9y7dw+ffPIJWrduXRl7I1wI08zaiOb1zLJ2k5KSwH2uuVk7BqFQiPXr17PWy84zuUZrmz7Wo7dqBoX525RJTFQ+JVowq1atwgcffIDWrVvj8uXL+PDDDzF16lS0b9++MvZHuAjWck/0Wbtr/r6CWzv2Qq1WwTs4ElyBCFqVApobF3H27Fmj8SM1vT1w46HC6HFp3ptwPCUKzPr169m/N23aFN999x3Gjx9PAkOYYZp7Ypi1W6RhwPdrgYL9Sbi7azHbjmH6uz2MxAUAPnirMcb+eBpqLQM+l4MP3mps93sTzkGp2jUoFAqIRKKK2I9dUBTJuUnNyMP7m85AodZCq1IYlQEAgEgkQnZ2tk1RI8I1KVUtkjOIC1F2KvpLHNncFz0ld7FmzxG2M51hUeMnn3xidbYRWSTugVMVOxKVR3ED6cuTwsvHcH9/EsSBbVGn58e66FHLKBRdP4dmb9FsI3fHqfrBEJVHZfS2TUlJwY8HzqNmxGh4t+zyLHrEF0L8YhvM/O0q5ay4OWTBVFEquqVBZmYmxsxdyea8aNVKMGolOHwhe49cpcGmE9fJ1+LGkAVTRdGHdoe29y/341FKSgpCQ0PBe76FkdVSlH0egZ4Ktq6IMnDdH7JgqjAV4UiVyWSIj49HUVERuNJ0o5wXxaU/kLLyPZyVaSkDt4pAAkOUK1KpFDyeLqtWnpXG5rxoblzE6pkJkEgkiJSALYY8fvUedZ5zY0hgiDJhGupOSkqCpl5z1DSYa6TNOYf09HSzhDrKwHV/SGCIUmMa6h4bIsKmgxeMwtEK6VnEhNY3Exc9lO/i3pCTlyg1pqHuz77dClFAqJFj1zOwLf5X6EcO3CoKCQxRagwrqBmVAk+unoZCms7OltajYjg0Q7qKQgJDlBq9DyVAdR2yXYsBAKKAUDw6uRNPstLAqJUAqIVCVYZ8MIQZ9tQobV42HQfXrjUqBdCqFLj/6zLMiA3HXX4dcuBWYUhgCCPsqVHKzMzE2rVrAcDY9yIQoVO/URj/9huVtW3CSaEjEmGELTVK+nEhK7b+wV4z9L1oVQrEdX+1cjZMODVkwRBGlFSjtGTfZaw+eAUaLQOtqj7EgW0hz0ozSqqLfSME/drT2F+CBKbKY+pvKS75zbAZN/Cspy4AtkNdn4YqrPxkjNX1y7o/wrUoVUc7Z4E62pUNQ3+LWMCz6m9JzcjDphPXcfBfGbQGvy36aYw+bXqDKxCBDy1WDW3LrmHr+mXdH+G8kA+mCmOrv2V8SjoOXDYRF60WD09sB9fDi3XuqsE1WqOsPWcqo2cNUbGQwFRhTEeNWMpVMfyS62E0ajw8vhUPD/1o5Nw1XcOW9cu6P8K5oSNSFackH4fhMYUHBoVXTqPg7G9GzbvFgW3ReegHSHj7LbM1yAdTtSGBIUokNSMPu078i3WLp6HgnyMW78nIyLBa0EhUXSiKRJRoJdw99ydWjRwCjUZj4dXAuHHjSFwIi5DAVHEMj0Abj1/HmDcCjeZAy2QyDB8+3KK48Pl8/PXXX+jQoYPFdeloQ5CTt4pj6MTVMMDqg1eMWiskJSWhqKjI4mtnz55tVVzGp6RTr12CBMbd0af1W/uSd2osMfol0GgZNhwsk8kwf/58i68TiUQYPXq0xecovEzoIYFxY2y1JLhcDvt3IY/LhoOXL18OhUJhdr9301fR67ONOCvTWhQwCi8TesgH48ZYsiRM/SGH/pNBbZBB1yGwNiKb+2LS8nVYe+o+W2ukp1qzDqjfdzqO5zM4s/EMAECp0RpVXlOvXUKP01gwDMOgU6dOGDJkCIYMGYJly5Y5eksujy2WhOk9g8L8sf3Yv9h6wxs+r/RAnZ4fQxzYlr3/pV6jUKTRCZJSo4VSowVgfhSKbO6Lz3q1IHGp4jiNBZOdnY2XXnoJq1evdvRW3AZbLAlL97wy8gdwa7cA8KygUZ6VBnFgW8g4tYGnBg+fywGXw4FSo6WjEGERpxGYS5cuIS8vD0OGDIFIJMK0adPwwgsvOHpbLo+1rv2WqqgBXROpzL92oE7PQLY7nbboMWpGjIagRj2oDdIyOzWug0Fh/nQUIqziEIHZtm0b1q1bZ3Rt1qxZGDVqFLp27YpTp05h8uTJ+OmnnxyxPbenuK51SUlJkGel4dHJnRAHhkGVn8NWS3OhBZ/HZS2WQWH+NHaEKBaHCExMTAxiYmKMrsnlcnYiYOvWrZGXlweGYcDhcCwtQZQBa87fwYMHY9OmTRAHtmVFRVi7ATg83a+JFlw0reeN0IY1yWIhbMJpnLxff/01a9X8888/eO6550hcKghLzt9Bgwbh57Qs1IwYDe+WXdgWDBweH4xBFu/l24UkLoTNOI0PZtSoUZg8eTIOHjwIHo+HhQsXOnpLLktJafqmjl0/zj3sPHnl2VQAtRKMWgkOXwitSoGaXAUeogYAXeSIhtQTtuI0AlO9enV8++23jt6Gy2PrVABD38m6dXvNJjI+yUqD+mEeIl9ugBHDRxh1lqNoEWErTiMwRPlgLU2/OItGJpNBIU2Hd3AkGzkqPLcX8qw0zPkqA0FBOotn04nrlfqzEK4PCYwbYHgkMp0KUE0kKNaikclkmDVrFuRyOTsVQCFNhzwrzawNw/Gr9yBXaXD86j3qj0vYBAmMi2PpSGRobWTcfFhsuUB6ejq4XJ2vXz9+xMPDA1u2bEH//v3Z+2wpOyAIU5wmikSUDktf/LM5D/D3f3dx4LIMR7LyIeTp/jcLeVzk3HvCFiYuXboU0dHRePz4sdGaXC4X4eHhRteslR2UVK1NVG3IgnFxLB2JVv+VhaflQlBqtAhvqhODI1n5OHBZhuNX76FJ/mHsWmXeikEsFiM5ORkSyTMB0R+/TEsK7BkzS1RNSGBcHNOQ86H/ZKy4AACPy2HT+ZUancNXrtLg2B2e2VpisRg7d+5E586dAVg+fn3WqwV7/6YT1+nYRBQLCYwbYJqur7doeBxgzOsvss9tTsthq5/FASFmrRg0Gg1CQ0NZqyXn3hOrApKakYcjWfnsaw37yBCEHhIYJ6G8ethaq6CObO6LDoG1ceCyzorh8IVslbSe+fPn46xMy1otQh4XQoPaI0MB0VlEWvaxvo8MQRhCAuMElLcvw1oBoufNM9CqJGyui0Kazj7XqVMnTJo0CbN+uchaLXr/TYNanmbCZ+r7GRTmX+r9Eu4LCYwTUBkhYJlMhm/nvA9BQCujXBc9SUlJACwLh619ZAjCFBIYJ8D0S11aX0Zxxyx9vos+18WQqKgoNqHOHuGgVg1ESdBkRyehPEasGtYLGR6zZq7ehqSdB1F45aSZuHA4HOTl5VkMS5N4EGWFLBgnoazWgLVj1vZj/2Ldf1x4hnSFqMVbUEjPsnVGfD4f69evNxIXymshyhMSGDfB2jFrz6ksoyppz8C2EPkHo4vPLcx/bwArLgCVAxDlD5UKuDj6VH0A+Co2FEPb+xtZHteO/Q6tyni2EVcggrLWC0biAtA8I6L8IQvGRUnNyMOmE9dxJCvfaC6RYabtkSNH8HfK1xAHpsG7ZReIG7XSdahTKxHd+iWzNSkyRJQ3JDAuhqmw6DE90qSkpODdd9/VPffUsSsKCAEHAJfHQ/Xq1S2uT5EhojyhI5ILoXfCHrhsnEULGB9pZDIZ3n33XahUKvZ5UUAouHwhAIDh8GheNFEpkMC4CKkZeVi67x/WCatHyOMivKnEyO8yffp0I3EBAIU0nfXFkH+FqCzoiOQCGIaP9Qh5XHQIrG2WaTtixAgkJyebrSHPSsPAhk8gCmhK/hWi0iCBcTC2JLYZho8BoKmvNyZFNTO7PzMz06K4AIBAIMDkQV0gkUjYyBMJDVHR0BHJgegtk/XHrmN8SrrVrnCm4WNL4pKakYe+8zcbDao3JDExkRUXW96TIMoDsmAciC2JbXoLJ65jI2TcfGhxndSMPIxdnwa1X1vU8Q3Go5M7wfXwYgsaR4wYgdGjR9v8ngRRXpDAOJCSihwNfS/6vrpKjdasq///zmdD/dQY5QpEqN6uPzhcLryDI5G/eykWLFhg9T2riQR0XCIqDBIYB1JSYpuhtVFczsvhA/vB+DTXJdExDDjcZ2LTtudQo4xdw/esJhJg7eFrVHtEVBjkg3Ewkc198VmvFha/2Ia+F313OcA4zPz9vlO44d1EJy5ardE8b0ajRsLbbxmtaehULlCoLA5pI4jygiwYJ8bUwgFgNl3xuz2HwfVqDADgcLlgNOqnA+vVCK+vQb/2Tdh7Taul4zo2gljAo5GwRIVBAuPkGKbup2bkGU1X7F4zD2f3pjwbWq9SsA7eOWMGYvzbbxitZergLVCoqPaIqFBIYFwIU4H4Ye9xyLPSzEa+xsTEmIkLYNmpTLVHREVCAuNCGAqEgKPFk2tnAMCoDaZAIMDKlSstvp6qpYnKhgTGhdALxPzkn5C2a51Z+0sA+Oijj8z6vJiuQcJCVBYkMC6GH+ceDi5PsPicQCDAxIkTK3lHBGEdEhgnx7RWKS3N3GoBdOKybt26Yq0XgqhsSGCcGEtNuAMDAy3euzTlf8jk10FqRh4dgQingRLtKgF99bK9hYWmUaPkX48gMjISAoHA6L5+H3yKVWcVVMBIOB0kMBVMWaqXDTN5RXwu9v7wBeRyOdtMSiAQf1zOWAAAEmdJREFU4PDhwwgK70sZuYRTQgJTwViqXjYlNSMPw79Pw/Dv04wESB81GtreH3FBHKivnzF6nVgshlAopGkAhNNCPpgKxpaK6YSNZ9hixiNZ+Vg5uBXrR4ls7ou75/5E/Mh4yOVyo9eqVCoEBARAIpFQfgvhlDhUYFJTU7F3714sW7YMAHD27FnMnz8fPB4PHTt2xLhx4xy5vVJhGvWxpWLasFJaqdEaVUrLZDLEx5uLi0gkQnJyMhs1ovwWwhlx2BFp3rx5WLZsGbTaZ1+u2bNnY9myZUhJScG5c+dw6dIlR22vVJTG39KpsYStkgZ0/0OqiZ45cX/55RejzwgAvLy88Oman5Hp+TI5dAmnxmEC06pVK8yZM4d9XFhYCKVSiYYNG4LD4aBjx444duyYo7ZXKiz5W0oSncjmvlg5uBVeft4HXA6gBbD28DWkZuShc+fOGDlyJIqKioxew/dvhbWZDEWNCKenwgVm27ZtiI6ONvpz/vx5dOvWzah3SWFhIby9vdnHXl5eKCgoqOjtlSuWnK22OHkjm/sitGFNaBmw9239+zxSU1PN7vXw8ECXYROgUGuLXZMgnIEK98HExMQgJiamxPu8vb3x+PFj9vHjx4/h4+NTkVsrd6z5W4pz8uoxdQZf3L/d4n3jxo1DVPcOOPc0AY+iRoQz4zRRJG9vbwgEAmRnZ6NBgwY4fPiw0zl5bRkxYupstbWC2fC+s3s3Y/dP30Ic2NaoDQMA9OnTBx2oKppwEZxGYADg008/xaRJk6DRaNCxY0e0bNnS0VtisZS2b+sX29YIT2RzX3jez8Lc1fMhDmzLNpLyDo7E3V2LEVybgw4dOpT1RyGISsOhAhMWFoawsDD2cUhICLZu3erAHVmnMsZ9GA6sFwWEgisQAdA17/Zs1Aq7N34GoGxiRxCVCWXy2khFZ8vKZDIMGTKELQMwnCWtVSkw4PWWbM6LLY5jgnAGnOqI5MxUdDe4efPmQdjoFSOfi74VZsfAOli5bB57b0nZwQThLHAYhmEcvYnS0rdvX+zYscPR27AZa05imUyGgA49ULvHZLZ5991diwEAYb2GoVvkmyhQqIxeZ4vDmSAcDVkwlURxfpMDBw7Awz/EyOfi3bILRAEhuMYXYuWBLAAweh2VBhCuAAlMJWHqN9l04joO/SfDkyun8dXUkeD7h8I7OJK1YHieNcDlC43WoFnShKtBAlNJGPpNhDwujmTlQ6mRQavyBt8/1Gz8iHfLLmZrkL+FcDUoilQG7OlUZ9jbpUNgbbaCmisQQRQQCkA3fuT+/iSopGcw9NUX2CJIPpeD8KYSCkcTLgdZMKWkNLkoer/Jkn2XcfBfGbSMLgStkKaz9wgEAiTtPoprChFGviQwc+4ShCtBAlNKSpN4l5qRh00nruNIVj60jG44/aOTO43mGw2YOB+LD99lQ9BktRCuDB2RSom9iXd6i+fA5WcNpjg8PrgeXuw9PB4P9ULeoCQ6wm0gC6aU2Jt4Z2jx6DE9Hs2ZMwdhwQ2x51I+JdERbgEl2lUShj4brVoJhfQsCs/tZY9HQqEQubm5kEgklERHuA1kwVQSeovn+9+OYWfSIrO50hMnTqT+uoTbQQJTRuyxNq4e2okdMz4wa4FJM6UJd4UExk4MBQWAzaHqpKQkjBkzhn2sbyalvXEJq2a+RzOlCbeEBMYOTHNf2r1Qq8RQdWpGHv53PhtJX2xgrxk2kxK26YE6LVtX6s9BEJUFhantwDT3BUCxoWq9IG07ewc1un0IcWBbAMbNpJRaUCiacFvIgrED0z4sg8L8MSjM38wHoz9G5dx7wgqRviRAnpWmqzV6WthIoWjCnSGBsQNruS+GxyLDY5SAywGjVoLDFxrlvMiz0vC64Coate9KoWjCrSGBsZOSQsiGxyiVloFcehbqh3lGkwF8gjqgXsgbJC6E20M+mHLGsIRAq1Kg8Nxe3N+fxIqLOLAtJL2mYNvZOzSVkXB7SGBswN62DHO7vYDCM3twd9dis4S6kC6xUDO6j51qjQh3hwSmBKzNli5OdHwKpMhPXW0mLgAwMrpjhU4nIAhngnwwJWBtREhp5hL17NkTw6Naw68B1RoRVQOyYErAnoH2MpkMJ0+eRIMGDSAQCIzW4fF4WLNmDQDdMeqzXi1IXAi3hyyYErB1oH1KSgqGDx8ODocDhmEwevRorFmzBjweDxqNBmvXrqVyAKLKQe0aSolhTVKIhAtfX18YfpRcLhcXL15EYWEhAgICrIoLtWYg3BmyYEqJYT7MyJEjYarTWq0WFy5cQP/+/a2uQTOmCXeHfDBlZNLydfhJymPrjABdrkvNiNHYn3mn2NfSjGnC3SGBKQPbj/2LrTe84fNKD9Tp+THEgW3ZSmmfV3rggCKg2NwZe/v6EoSrQUekMrDnVJbZuFf1wzz2morhsC0cLPla7O3rSxCuBlkwZaB5LS60aiX7WBwQAm3RY2hVCt3jp1aJtWQ9gELWhHtDAlMGhnd+Bcrs8+xjDl8IvrgaPu3sj6Ht/VmnLflaiKoKHZHKgEQiwcg3m2P9f0XgCDzAqIowtk84hkcZd6gz7SNDvhaiqkACUwpkMhmkUikCAgIwd0wMWh77F6kXcxDZojH6tW9idj/5WoiqCgmMnaSkpCA+Ph5CoRBKpRLJycmIjY21KCyG0CgSoipCPhg7kMlkiI+Ph1wux8OHDyGXyxEfHw+ZjHwqBGEJhwpMamoqPvroI/bx//73P0RERGDIkCEYMmQI0tLM2x04kvT0dHC5xh+ZQCCAVCot07r29JshCFfCYUekefPm4fDhwwgKCmKvXbp0CZMnT0ZUVJSjtmWVpUuXYvr06VCpVEbXVSoVAgICSr0ulQsQ7ozDLJhWrVphzpw5RtcuXbqEn376CYMGDcKiRYugVqsdszkTRowYgcmTJ5uJi1gsRnJycpmqpCmETbgzFS4w27ZtQ3R0tNGf8+fPo1u3buBwOEb3dujQATNnzsTGjRvx5MkTbN68uaK3VyKZmZlITk42uy4Wi7Fz507ExsaWaX0qFyDcmQo/IsXExCAmJsame99++234+PgAAN566y3s27evIrdmE/v377d4Xa1WIzQ0tMzrUwibcGecJkzNMAx69uyJzZs3o169ejh27BheeuklR2/L7JimnyndLqA6zsq0OHT0YrHCYEu/FwphE+6K0wgMh8PBvHnzMG7cOIhEIrz44ovF9lKpLPj8Zx+R4Uzpf6BFwsYzUGq0Vp2z5MAlqjoOFZiwsDCEhYWxjzt27IiOHTs6cEfmREREsH83nCmtBRdKjRaA9cH3lhy4JDBEVYIS7UogKCgI48aNAwAopOlspbSQx4WQp/v4uADOZD/Akn2X2XyW1Iw85Nx7wt5DDlyiKkI9eW0kMzMTaWlp0NZ7CdcUInRqLMHZnAdY9VcWtCafoF5UlBothDwuOgTWxqAwf7JeiCqH0/hgnJ2goCCjpEBAdwQyFRcA7NFJ//cGtTxJXIgqCR2RykCnxhLWWjHE8PhERyOiKkMWTBmIbO6LlYNbYdOJ6wCA5s9VR4FCxQoK5bYQVR0SmDJSXA4LCQtR1aEjEkEQFQYJDEEQFQYJDEEQFUaV98HIZDKkp6cDAEJDQ2lAPUGUI1XagklJScHzzz+PqKgoREVFwc/PDykpKY7eFkG4DVVWYGQyGeLi4oyaSCmVSuqxSxDlSJUVGKlUCh6PZ3ady+WWuccuQRA6qqzABAQEQKPRmF3XarVl6rFLEMQzqqzASCQSrF27FgKBgL0mFArL3GOXIIhnVOkoUmxsLCIiIkqMItnSlY4gCHOqtMAAOkumc+fOVp+nrnQEUXqqvMCUhGlXuk0nrpM1QxA2UmV9MLZiOFZEyOPiSFY+1h+7jvEp6TSJkSBKgASmBPRjRYa290eHwNpmfXgJgrAOHZFsQN+SITUjD8ev3oNcpaFGUgRhA24vMDKZDFKpFAEBAWUOP9OQNIKwD7cWmJSUFMTHx0MoFEKpVCI5ObnMo15pSBpB2I7b+mBkMhni4+Mhl8vx8OFDyOVyqjMiiErGbQVGKpVCKBQaXRMIBFRnRBCViNsKTEBAAJRKpdE1lUpFdUYEUYm4rcBIJBIkJydDLBbDx8cHYrGY6owIopJxayevvtaovKJIBEHYx//bu7eQKLoADuD/acuKtqgHH7qoWRhR0A2xHlbfYimiIhooyIhMt6J7bm6Bl8rWHjLDpIUgogv0YAXfm+VT3iowWmG3XL4ITV+2JXpwbKNyz/fgx2Dm1hZ79szG//e2ozh/hvHvOePMnL+6YIDRkQyLhUiNv3aKRETqsWCISBoWDBFJw4IhImlYMEQkDQuGiKRhwRCRNCwYIpKGBUNE0ii5k3doaAhutxuGYeDr16/weDxYvXo1/H4/Lly4AJvNBofDgUOHDqmIR0RJomQEc/PmTaxbtw53795FXV0dzp07BwCorq5GfX097t27h56eHgSDQRXx/kjrqzCq/gnwReBEYygZwezZs8d8V8vIyAimTp0KwzDw5csXZGdnAwAcDgeePn2K5cuXq4j4W7h2EtHEpBdMc3Mzbt269d02r9eLFStWIBKJwO1248yZMzAMA3a73fyeGTNmYGBgQHa8pBi/dlL7vxEWDBFSUDC6rkPX9R+2h0IhnDhxAqdOnUJBQQEMw8Dw8LD59eHhYcyaNUt2vKQozMtEc/cgVxsgGkfJFOnNmzc4evQorly5gqVLlwIA7HY7pkyZgnfv3iErKwsdHR1pc5GXqw0QTUwTQohU7/TAgQMIhUKYP38+gNFy8fl88Pv98Hq9GBkZgcPhwPHjx3/6c7Zt24aHDx+mIjIR/QElBZMsLBgia+ONdkQkDQuGiKRhwRCRNCwYIpKGBUNE0rBgiEgaFgwRScOCISJpWDBEJA0LhoikYcEQkTQsGCKSJq0fdly7dq35RDYRqTNnzhzcuHHjh+1pXTBEZG2cIhGRNCwYIpKGBUNE0rBgiEgaFgwRScOCISJplCxbkm5aW1vR0tKC+vp6AEibNbSFECgqKsLChQsBAKtWrcLJkyfVhoojFouhpqYGoVAIGRkZqK2tRU5OjupYCdm6dStmzpwJAFiwYAHq6uoUJ4qvp6cHly5dwp07d9Df3w+PxwNN05CXl4fq6mpMmpTkMYegnzp//rxwOp3i2LFj5rbNmzeL/v5+EYvFxL59+0QgEFCYML6+vj7hcrlUx0jIo0ePREVFhRBCiJcvX4r9+/crTpSYz58/iy1btqiOkZDr16+LTZs2CV3XhRBCuFwu8ezZMyGEEJWVleLx48dJ3yenSL+wZs0a1NTUmJ/HrqGtaZq5hrYVBYNBhMNhFBcXo7S0FG/fvlUdKa4XL16gsLAQwOhIKxAIKE6UmN7eXkSjUezduxe7d++G3+9XHSmu7OxsXL161fwcDAZRUFAAACgqKkJXV1fS98kp0v/iraG9ceNGPH/+3Nxm1TW0J8pfVVWFsrIybNiwAd3d3XC73Xjw4IGihD83/rjabDZ8+/YNkydb+xSdNm0aSkpKoOs6+vr6UFpaipaWFkvmdjqdGBwcND8LIaBpGoDR83hoaCjp+7TeUVAk3hra49ntdkuuoT1R/mg0CpvNBgDIz89HOBz+7qSykvHHNRaLWfKXdLzc3Fzk5ORA0zTk5uZi9uzZiEQimDt3rupovzT2eous85hTpN80dg1tIQQ6OjqQn5+vOtaEmpqazFFNb28v5s2bZ8lyAUanom1tbQBGL6IvWbJEcaLE3L9/HxcvXgQAhMNhGIaBzMxMxakSs2zZMnN03tbWJuU8tv6fCAs6e/YsysvLzTW0V65cqTrShMrKyuB2u/HkyRPYbDZL/3dj/fr16OzsxI4dOyCEgNfrVR0pIdu3b8fp06exc+dOaJoGr9ebFiMvAKioqEBlZSUuX76MRYsWwel0Jn0ffJqaiKThFImIpGHBEJE0LBgikoYFQ0TSsGCISBoWDBFJw4IhImlYMJRSxcXF6OzsBAA0NDSgtrZWcSKSKT1uOaS/xpEjR9DY2IgPHz7g9evX8Pl8qiORRLyTl1Ju165d+PTpE27fvg273Y6BgQH4fD4YhoHGxkbV8SiJOEWilAqFQohEIsjIyDBfz5CVlZU2zx7R72HBUMq8f/8e5eXluHbtGqZPn4729nbVkUgyFgylRDQaxeHDh+HxeLB48WIcPHgQTU1NqmORZLwGQ8p9/PgRDQ0N6Orqgq7rcLlcqiNRkrBgiEgaTpGISBoWDBFJw4IhImlYMEQkDQuGiKRhwRCRNCwYIpKGBUNE0vwHhYA1GBJBk+cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 288x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "recovered_data = projection1D.dot(pc1.T).rename(columns={0: '$x_1$', 1: '$x_2$'})\n",
    "\n",
    "rms_reconstruction_error = np.sqrt(np.mean(np.sum(np.square(recovered_data-data_), axis=1)))\n",
    "\n",
    "rss_data = np.sqrt(np.sum(data_.values**2))\n",
    "\n",
    "relative_loss = rms_reconstruction_error / rss_data\n",
    "\n",
    "title='Reconstructed Data | Error: {:.2%}'.format(relative_loss)\n",
    "ax = recovered_data.plot.scatter(x=0, y=1, title=title, c='k')\n",
    "ax.set_aspect('equal')\n",
    "data_.plot.scatter(x=0, y=1, s=10, ax=ax, figsize=(4,8))\n",
    "plt.legend(handles=[Patch(color='k', label='Recovered'),  \n",
    "                    Patch(label='Original Data')])\n",
    "sns.despine()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Projection and inverse transformation lead to the same result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-18T13:40:49.481437Z",
     "start_time": "2020-06-18T13:40:49.478027Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(recovered_data, X_.dot(pc1) * pc1.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
